Use the van der waals

Question

^{use the van der Waals equation of state to calculate the pressure of 3.30 mol of NH_3 at 499 K in a 5.90-L vessel?}

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^P=

^{Use the ideal gas equation to calculate the pressure p under the same condition}

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^P=

^{Please help I tried everything and I keept getting it wrong
}

Answer 1

Ideal gas law:

PV = nRT

P = pressure =?

V = volume = 5.90 L

n = moles = 3.30 mol

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 499 K

Solving for P we have..,

(P)(5.90) = (3.30)(0.0821)(499)

P = (3.30)(0.0821)(499) / 5.90

P = 22.9 atm

van der Walls equation:

(P + an² / V²) (V - nb) = nRT (note that the left side of the ideal gas law has correction factors for P&V)

P = pressure = ?

a = 4.17 L²atm mol^-2 (value for NH₃ looked up online)

V = volume = 5.90 L

n = moles = 3.30 mol

b = 0.0371 Lmol^-1 (value for NH₃ looked up online)

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 499K

Solving for P, we have...

P = nRT / (V - nb) - an²/V²

P = (3.30)(0.0821)(499) / (5.90 - 3.30*0.0371) - 4.17*10.89 / 34.81

P = 135 / 5.78 - 1.30

P = 22.1 atm